Chi Boots + Cold Weather Housetraining Advice Needed!

Backstory: Odie came to us pee pad trained. She's 100% trained, but will go to the bathroom when we go outside too. We've been slowly trying to phase out pee pads the past few months (we don't crate her). For the past week, she's has had no access to a pee pad and has only had two accidents which is definitely progress. However, we live in Canada, and it's starting to get cold. We don't have a yard, so when we take her out she has to go for a little walk. Lately, we've been carrying her to the shoveled area to avoid the salt melt they put on the cement and pick her up when she's done. She usually pees quickly and I pick her up and go back in right away.

Today I took her out in the afternoon and she wouldn't go to the bathroom. She was just trying to stand on my shoes which she's never done before, and after about a half a minute of that, it was almost like she fell forward onto her belly, and she started whining and wouldn't get back up. I picked her up immediately and warmed up her feet (they were really cold). We're going to get her a custom made waterproof winter jacket, but what i'd like to know is has anyone found good quality boots suitable for a chihuahua? Ones that are semi-easy to put on?

I know that she won't like them at first, but I feel like we're really making progress getting rid of of the pee pads and I don't want to just go back to them. I've tried all the pet stores in town and i've found some really nice ones, but not small enough for her. Someone suggested socks to me, but I don't really think that's going to cut it. We do have a covered patio (not enclosed, just covered) that I could put a pee pad on. Maybe if I put a pad out there, she would still associate the cold with outside but wouldn't have to be out there for as long? Winters are usually mild here, but sometimes we get cold snaps and temps drop to -30 and i've heard of pets getting frost bite easily. We want to be prepared!